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WAEC 2016 Mathematics · Question 30

Simplify (p−r)2−r22p2−4pr\frac{(p - r)^2 - r^2}{2p^2 - 4pr}

Options

  1. A.12\frac{1}{2}
  2. B.p - 2r
  3. C.1p−2r\frac{1}{p - 2r}
  4. D.2pp−2r\frac{2p}{p - 2r}

Answer: A. 12\frac{1}{2}

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need to simplify a fraction. The numerator is a difference of two squares, and the denominator has a common factor. Step 2: Concept Difference of two squares: a² − b² = (a − b)(a + b) Step 3: Solution Numerator: (p − r)² − r² = [(p − r) − r][(p − r) + r] = (p − 2r)(p) = p(p − 2r) Denominator: 2p² − 4pr = 2p(p − 2r) So the fraction is: p(p − 2r) / [2p(p − 2r)] Cancel p and (p − 2r): = 1/2 Step 4: Answer Check with numbers: Let p = 3, r = 1. Numerator: (2)² − 1 = 3 Denominator: 2(9) − 4(3) = 18 − 12 = 6 3/6 = 1/2 ✓ Tip: When you see "something squared minus something squared," immediately think difference of two squares. Then look for common factors in the denominator, because the factors usually cancel neatly.

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